Is it a mitzvah or praiseworthy to live in Jerusalem relative to any other part of Israel?
ב"ה This question really gives me great pleasure to write about the Kedusha= holiness of Jerusalem. But I will try to be short and to the point. The Mishna says Ketubot 13: 11 says that "all may force their family to ascend to Jerusalem." This Halacha is brought down in Shulchan Aruch Even Ha'ezer 75. The Avnei Nezer, Rabbi Avraham Bornstein of Sochatshuv, (18th century Poland), wrote that it is a mitzvah to live in Jerusalem which a holy place , a sanctified place with the Divine presence. The Chatam Sofer , RaV Moshe Sofer , 19th century, Slovakia- then Hungary) writes that Jerusalem is the gateway to heaven and the holiness of Jerusalem is an everlasting one. The mitzvah to live there has to do with its own innate holiness and not because of the Mitzvot which can be done there. In practical terms, in our time Rav Eliezer Waldenberg zt"l, wrote in Tzitz Eliezer Vol. 14: 52 , that it is a Mitzvah to live even in the new neighborhoods of Jerusalem which are adjacent to the most sanctified places. The sanctity being eternal and heavenly. All the best Shabbat Shalom and Shanna Tova